Nothing special on the Georgian part. Just the booth, show your ID or passport and you are free to go.

On the Russian side I waited about 30min in line to enter the area.
A police officer went through the waiting line to hand out the immigration card to fill out.
I was allowed to cut the line (by about 10 cars) with my bike.
At the first booth it’s the usual passport, visa and immigration control. I didn’t have any hotel reservation, so I’ve just written the hostel name in Volgograd on the immigration card. I was planning to stay there anyways.

At the second booth you are supposed to fill out the passenger and vehicle import declaration. In my case the booth was not occupied and I almost went through customs without it. An officer talked to me while I was getting ready to drive off and asked if I know about this declaration, so he guided me to another booth to get the paperwork.
You can download and print it out beforehand here (two copies required!).
There was no defined waiting line at this booth, just a few people in front of it. I waited until the small window opened and quickly handed the paper in, before any other one had time to react. It takes them 10 minutes per declaration, so I really saved time here.

When leaving the area there’s another passport and immigration card control.
It took me about 1.5h to get through the whole crossing.

After about two kilometers there were a lot of small container buildings. I tried some of them which had an English sign with ‘insurance’ written on it until one could sell me a motorcycle insurance. It was 900 rubles (about 15 CHF) for 15 days. They didn’t speak English, but we managed it anyways. Not sure if I really have a correct insurance, though…

About 4-5 kilometers later there was a police control. They put me on a fake alcohol test and wanted to keep my drivers license. I had to pay 5000 rubles bribe to get my it back!